Computational investigations of folded self-avoiding walks related to protein folding

Various subsets of self-avoiding walks naturally appear when investigating existing methods designed to predict the 3D conformation of a protein of interest. Two such subsets, namely the folded and the unfoldable self-avoiding walks, are studied computationally in this article. We show that these two sets are equal and correspond to the whole $n$-step self-avoiding walks for $n\leqslant 14$, but that they are different for numerous $n \geqslant 108$, which are common protein lengths. Concrete counterexamples are provided and the computational methods used to discover them are completely detailed. A tool for studying these subsets of walks related to both pivot moves and proteins conformations is finally presented.